Maximal (k, n)-arc in Projective Plane PG(2, 5)

Abstract

In this paper we recognize maximal (k, n)-arcs in the projective plane PG (2,5), n = 2, 3, ...,5, where a (k, n)-arc K in a projective plane is a set of K pointssuch that no n + 1 of which are collinear. A (k, n) – arc is a maximal if and only ifevery line in the projective plane PG (2, P) is a O-secant, or n-secant, whichrepresented as ( k, 2 )-arc and (k, 6)-arc. A (k, n)-arc is complete if it is notcontained in a (k + 1, n) – arc.